A variety of error sources limit gate fidelities in experiments, including imperfect Rydberg blockades, decay of the Rydberg state, scattering of an intermediate state in a two photon transition, laser phase noise, variations of the laser intensity with the position of the atom in the trap and Doppler shifts of the laser frequency due to thermal motion of the atoms [1]}, [2]}, [3]}. To mitigate the effects of these errors, many different improvements of the original protocol [4]} have been proposed based on adiabatic passage [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, dark state mechanisms [11]}, Rydberg Antiblockade [12]}, [13]}, [10]}, and many other approaches [15]}, [16]}, [17]}, [18]}, [19]}. It is increasingly recognized that all these approaches can benefit from quantum optimal control methods to improve both the speed and fidelities of the various quantum gates. Quantum optimal control methods can also provide additional solutions that differ qualitatively from any of the known basic gate schemes.
